COASTER (both loops throughout)
1. Ch 4 sc, insert hook into the 1st st, sl st together to form a loop (you can also use a magic circle instead of chaining four together).
2. Ch 2 (do not count this st), crochet 16 dc into the loop, sl st into the 1st st to close the round. (16)
3. Ch 2 (do not count this st), crochet 2 dc into the same st you joined the round in, then in each dc from the first round, sl st to the 1st st to close the round. (32)
4. Ch 2 (do not count this st), crochet 1 dc into the same st you joined the round in, 2 dc in the next st, *1dc in the next st, 2 dc in the next st* until you reach the beginning of the round, sl st to the 1st st to close the round. (48)
5. Ch 1 (do not count this st), sc in each dc from the previous round, sl st to close the round.
6. Tie off and hide your ends!

COZY (both loops throughout)
1. Rows 1 & 2: Chain 11, sc in each st, ch 1, turn
2. Rows 3 - 30: sc in each st, ch 1, turn.
3. At the end of Row 30, turn the rectangle sideways so the long side is towards your left hand, you're now going to sc along the edge. Ch 1, then start in the 10th st of Row 30, push the hook through both loops & pull the yarn over the end, pulling it over the side. Sc 29 more sts along the long side of the rectangle until you reach st 1 of Row 1, completing the sc.
4. Ch 1, slip hook into the first st of Row 1, pull the tail over the hook, then push the hook into the 10th st of Row 30, yarn over into a sc. Continue joining Row 30 to Row 1 with sc until you reach stitch 10 of Row 1. If you keep pulling the tail into your stitches at this point, it will line it up better to finish off your ends later.
5. Ch 1, now finish off the other end of the sleeve with 30 sc st (do not join any further or it will seal off the sleeve making a pocket). Once you reach the end of the last long side, sl st to the 1st st of the row.
6. Tie off, finish off your ends. I usually turn the sleeve wrong side out, pull the last tail through to the back and using the back of the joining stitches pull the tails under the joining stitches midway and tie off in the middle. Turn it right side out.

I love this pattern, and cannot for the life of me remember where I found the ideas for it. I learned circles from a crochet book from the 70's that my mom gave me a few years back. Another benefit to this pattern is that it is endlessly customisable. Use different yarns, change colors on rounds/rows or on the last round of single crochet on the coaster or joining the cozy, I've even used fun fur yarns on the edging on both the cozy and coaster.